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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 92736.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.bh1 | 92736dz6 | \([0, 0, 0, -45581196, -118446524656]\) | \(54804145548726848737/637608031452\) | \(121848792331978801152\) | \([2]\) | \(6291456\) | \(3.0050\) | |
92736.bh2 | 92736dz4 | \([0, 0, 0, -10203276, 12544284944]\) | \(614716917569296417/19093020912\) | \(3648733117113434112\) | \([2]\) | \(3145728\) | \(2.6584\) | |
92736.bh3 | 92736dz3 | \([0, 0, 0, -2922636, -1749767920]\) | \(14447092394873377/1439452851984\) | \(275083723825829904384\) | \([2, 2]\) | \(3145728\) | \(2.6584\) | |
92736.bh4 | 92736dz2 | \([0, 0, 0, -664716, 178495760]\) | \(169967019783457/26337394944\) | \(5033154553885753344\) | \([2, 2]\) | \(1572864\) | \(2.3119\) | |
92736.bh5 | 92736dz1 | \([0, 0, 0, 72564, 15409424]\) | \(221115865823/664731648\) | \(-127032196174184448\) | \([2]\) | \(786432\) | \(1.9653\) | \(\Gamma_0(N)\)-optimal |
92736.bh6 | 92736dz5 | \([0, 0, 0, 3609204, -8461886704]\) | \(27207619911317663/177609314617308\) | \(-33941668588687859908608\) | \([2]\) | \(6291456\) | \(3.0050\) |
Rank
sage: E.rank()
The elliptic curves in class 92736.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 92736.bh do not have complex multiplication.Modular form 92736.2.a.bh
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.